Estimation of a semiparametric natural direct effect model incorporating baseline covariates

E. J.Tchetgen Tchetgen, I. Shpitser

Research output: Contribution to journalArticle

Abstract

Establishing cause-effect relationships is a standard goal of empirical science. Once the existence of a causal relationship is established, the precise causal mechanism involved becomes a topic of interest. A particularly popular type of mechanism analysis concerns questions of mediation, i.e., to what extent an effect is direct, and to what extent it is mediated by a third variable. A semiparametric theory has recently been proposed that allows multiply robust estimation of direct and mediated marginal effect functionals in observational studies (Tchetgen Tchetgen & Shpitser, 2012). In this paper we extend the theory to handle parametric models of natural direct and indirect effects within levels of pre-exposure variables with an identity or log link function, where the model for the observed data likelihood is otherwise unrestricted. We show that estimation is generally infeasible in such a model because of the curse of dimensionality associated with the required estimation of auxiliary conditional densities or expectations, given high-dimensional covariates. Thus, we consider multiply robust estimation and propose a more general model which assumes that a subset, but not the entirety, of several working models holds.

Original languageEnglish (US)
Pages (from-to)849-864
Number of pages16
JournalBiometrika
Volume101
Issue number4
DOIs
StatePublished - Dec 1 2014
Externally publishedYes

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Keywords

  • Local efficiency
  • Mediation
  • Multiple robustness
  • Natural direct effect
  • Natural indirect effect

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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